Math playing cards

ABSTRACT

Decks of addition, subtraction, multiplication, division, and number recognition playing cards cover all the numbers generally employed in teaching children basic addition, subtraction, multiplication, division, and number recognition skills and are suitable for use in playing a variety of well know card games such as War, Concentration, Old Maid, Go Fish, Rummy, Gin Rummy, 21, and Spit.

FIELD OF THE INVENTION

[0001] The invention relates to playing cards for use in card games (such as War, Concentration, Old Maid, Go Fish, Rummy, Gin Rummy, 21, Spit, etc.). The playing cards enable children to have fun playing card games while effectively reviewing math skills (such as number recognition, addition, subtraction, multiplication, and division) that they learn in school.

DESCRIPTION OF THE PRIOR ART

[0002] School Zone Publishing Company (“School Zone”) markets three decks of Math War game cards, namely, (a) Addition & Subtraction Math War, (b) Multiplication Math War, and (c) Division Math War. Each of these Math War decks comprises one answer card, one parent card, two wild cards, and 52 game cards showing the math problems set forth below in Tables A through C for the (a) Addition & Subtraction Math War, (b) Multiplication Math War, and (c) Division Math War, respectively. TABLE A Addition & Subtraction Math War Addition/Subtraction Math Problems 5 − 3 8 − 5 7 − 4 1 + 3 3 + 2  8 − 3 3 + 3 10 − 4 5 + 3 3 + 6 3 + 7 9 − 7 9 − 6 1 + 2 4 + 0 6 − 1  9 − 4 1 + 5  5 + 2 4 + 4 2 + 7 6 + 4 8 − 6 4 − 1 2 + 2 8 − 4 7 − 2 10 − 5 7 − 1  8 − 1 7 + 1 8 + 1 6 − 4 5 − 2 6 − 2 9 − 5 4 + 1  4 + 2 8 − 2  3 + 4 2 + 6 8 + 2 3 + 0 6 − 3 7 − 3 5 − 1 5 − 0  6 − 0 9 − 3  1 + 6 4 + 5 5 + 5

[0003] TABLE B Multiplication Math War Multiplication Math Problems 2 × 4 2 × 9 3 × 6 4 × 4 5 × 2 5 × 7 6 × 7 7 × 5 8 × 3 8 × 9 9 × 8 2 × 5 3 × 2 3 × 7 4 × 6 5 × 3 5 × 8 6 × 8 7 × 7 8 × 4 9 × 2 9 × 9 2 × 6 3 × 3 3 × 8 4 × 7 5 × 4 6 × 2 6 × 9 7 × 8 8 × 6 9 × 3 2 × 7 3 × 4 4 × 2 4 × 8 5 × 5 6 × 4 7 × 2 7 × 9 8 × 7 9 × 4 2 × 8 3 × 5 4 × 3 4 × 9 5 × 6 6 × 6 7 × 3 8 × 2 8 × 8 9 × 5

[0004] TABLE C Division Math War Division Math Problems  6 ÷ 2 24 ÷ 8 28 ÷ 7 40 ÷ 8 36 ÷ 6 28 ÷ 4 16 ÷ 2 64 ÷ 8 54 ÷ 6  9 ÷ 3 27 ÷ 9 32 ÷ 8 45 ÷ 9 42 ÷ 7 35 ÷ 5 24 ÷ 3 72 ÷ 9 63 ÷ 7 12 ÷ 4  8 ÷ 2 36 ÷ 9 12 ÷ 2 48 ÷ 8 42 ÷ 6 32 ÷ 4 18 ÷ 2 72 ÷ 8 15 ÷ 5 12 ÷ 3 15 ÷ 3 18 ÷ 3 54 ÷ 9 49 ÷ 7 40 ÷ 5 27 ÷ 3 81 ÷ 9 18 ÷ 6 16 ÷ 4 20 ÷ 4 24 ÷ 4 14 ÷ 2 56 ÷ 8 48 ÷ 6 36 ÷ 4 21 ÷ 7 24 ÷ 6 25 ÷ 5 30 ÷ 5 21 ÷ 3 63 ÷ 9 56 ÷ 7 45 ÷ 5

SUMMARY OF THE INVENTION

[0005] There are drawbacks to School Zone's Math War decks of game cards. First, neither the Addition & Subtraction Math War nor the Multiplication Math War nor the Division Math War decks of game cards cover all the numbers generally used in teaching children basic addition, subtraction, multiplication, and division math skills. More specifically, using the equations A+B=C, C−B=A, A×B=C, and C÷B=A to represent addition, subtraction, multiplication, and division, respectively, School Zone's Math War decks do not cover each variation of A+B=C or C−B=A or A×B=C or C÷B=A for all the numbers generally used in teaching children basic addition, subtraction, multiplication, and division math skills, i.e., all whole numbers of A and B within the range of 1 through 10.

[0006] Furthermore, as can be seen in above Tables B and C, School Zone's Multiplication and Division Math War decks do not contain an even number of cards for each multiplication product or division quotient. For example, in School Zone's Multiplication Math War deck, there are an odd number of game cards for multiplication products 6, 9, 16, 18, 20, 25, 27, 28, 30, 36, 40, 42, 49, 54, 63, 64, and 81. Similarly, in School Zone's Division Math War deck, there are an odd number of game cards for division quotients 4 and 5. Therefore, School Zone's Multiplication and Division Math War decks are unsuitable for use in matching-type card games such as Concentration, Old Maid, Go Fish, Rummy, Gin Rummy, etc.

[0007] Accordingly, there is a need for decks of addition, subtraction, multiplication, and division playing cards that cover all the numbers generally employed in teaching children basic addition, subtraction, multiplication and division skills and that are suitable for use in playing a variety of well know card games such as War, Concentration, Old Maid, Go Fish, Rummy, Gin Rummy, 21, and Spit.

[0008] The present invention solves the needs set forth in the preceding paragraph by providing decks of addition, subtraction, multiplication, and division playing cards that cover all the numbers generally employed in teaching children basic addition, subtraction, multiplication and division skills and that are suitable for use in playing War, Concentration, Old Maid, Go Fish, Rummy, Gin Rummy, 21, Spit as well as other card games. In particular, in a first embodiment of the present invention, the decks comprises N playing cards, where (a) each playing card comprises a playing face and a rear face, (b) each playing face displays graphics, (c) the graphics displayed on any particular playing face of any particular playing card comprise a representation of a single mathematical operation having a numerical value, and (d) the mathematical operation is selected from the group consisting of addition, subtraction, multiplication, and division. (As used in the specification and claims, the term “playing card” means a card that displays a mathematical operation having a numerical value and that is used in a card game in accordance with its numerical value.)

[0009] When the mathematical operation is an addition operation, at least each of the following addition operations is displayed on the playing faces of the playing cards of the deck:

[0010] Group A: 1+1, A_(a)+B_(a); Group B: 2+1, A_(b+B) _(b); Group C: 1+3, 2+2; Group D: 1+4, 2+3; Group E: 1+5, 2+4, 3+3, A_(e)+B_(e); Group F: 1+6, 2+5, 3+4, A_(f)+B_(f); Group G: 1+7, 2+6, 4+4, 3+5; Group H: 1+8, 2+7, 3+6, 4+5; Group I: 1+9, 2+8, 3+7, 4+6, 5+5, A_(i)+B_(i); Group J: 1+10, 2+9, 3+8, 4+7, 5+6, A_(j)+B_(j); Group K: 2+10, 3+9, 4+8, 5+7, 6+6, A_(k)+B_(k); Group L: 3+10, 4+9, 5+8, 6+7; Group M: 4+10, 5+9, 6+8, 7+7; Group N: 5+10, 6+9, 7+8, A_(n)+B_(n); Group O: 6+10. 7+9, 8+8, A_(o)+B_(o); Group P: 7+10, 8+9; Group Q: 8+10, 9+9; Group R: 9+10, A_(r)+B_(r); and Group S: 10+10, A_(s)+B_(s), where

[0011] A_(a)+B_(a) is selected from the group consisting of 1+1 and 2+0;

[0012] A_(b)+B_(b) is selected from the group consisting of 1+2 and 3+0;

[0013] A_(e)+B_(e) is selected from the group consisting of 5+1, 4+2, 6+0;

[0014] A_(f)+B_(f) is selected from the group consisting of 6+1, 5+2, 4+3, and 7+0;

[0015] A_(i)+B_(i) is selected from the group consisting of 9+1, 8+2, 7+3, 6+4, and 10+0;

[0016] A_(j)+B_(j) is selected from the group consisting of 10+1, 9+2, 8+3, 7+4, 6+5, and 11+0;

[0017] A_(k)+B_(k) is selected from the group consisting of 10+2, 9+3, 8+4, 7+5, and 12+0;

[0018] A_(n)+B_(n) is selected from the group consisting of 10+5, 9+6, 8+7, and 15 +0;

[0019] A_(o)+B_(o) is selected from the group consisting of 10+6, 9+7, and 16+0;

[0020] A_(r)+B_(r) is selected from the group consisting of 10+9 and 19+0; and

[0021] A_(s)+B_(s) is selected from the group consisting of 10+10 and 20+0; and

[0022] N is at least 66. (Since A+B=B+A (where A is any number and B is any number), as used in the specification and claims, the addition operation “A+B” means A+B or its equivalent B+A. For example, the addition operation “5+4” means 5+4 or its equivalent 4+5.)

[0023] When the mathematical operation is a subtraction operation, at least each of the following subtraction operations is displayed on the playing faces of the playing cards:

[0024] Group A: 2−1, 3−2, 4−3, 5−4, 6−5, 7−6, 8−7, 9−10, 11−10; Group B: 3−1, 4−2, 5−3, 6−4, 7−5, 8−6, 9−7, 10−8, 11−9, 12−10; Group C: 4−1, 5−2, 6−3, 7−4, 8−5, 9−6, 10−7, 11−8, 12−9; 13−10; Group D: 5−1, 6−2, 7−3, 8−4, 9−5, 10−6, 11−7, 12−8, 13−9; 14−10; Group E: 6−1, 7−2, 8−3, 9−4, 10−5, 11−6, 12−7, 13−8, 14−9; 15−10; Group F: 7−1, 8−2, 9−3, 10−4, 11−5, 12−6, 13−7, 14−8, 15−9; 16−10; Group G: 8−1, 9−2, 10−3, 11−4, 12−5, 13−6, 14−7, 15−8, 16−9; 17−10; Group H: 9−1, 10−2, 11−3, 12−4, 13−5, 14−6, 15−7, 16−8, 17−9; 18−10; Group I: 10−1, 11−2, 12−3, 13−4, 14−5, 15−6, 16−7, 17−8, 18−9; 19−10; and Group J: 11−1, 12−2, 13−3, 14−4, 15−5, 16−6, 17−7, 18−8, 19−9; 20−10; and

[0025] N is at least 100.

[0026] When the mathematical operation is a multiplication operation, at least each of the following multiplication operations is displayed on the playing faces of the playing cards:

[0027] Group A: 1×1, 1×1; Group B:2×1, 1×2; Group C: 3×1, 1×3; Group D: 4×1, 2×2; Group E: 5×1, 1×5; Group F: 6×1, 3×2; Group G: 7×1, 1×7; Group H: 8×1, 4×2; Group I: 9×1, 3×3; Group J: 10×1, 5×2; Group K: 6×2, 4×3; Group L: 7×2, 2×7; Group M: 5×3, 3×5; Group N: 8×2, 4×4; Group O: 9×2, 6×3; Group P: 10×2, 5×4; Group Q: 7×3, 3×7; Group R: 8×3, 6×4; Group S: 5×5, 5×5; Group T: 9×3, 3×9; Group U: 7×4, 4×7; Group V: 10×3, 6×5; Group W: 8×4, 4×8; Group X: 7×5, 5×7; Group Y: 9×4, 6×6; Group Z: 10×4, 8×5; Group AA: 7×6, 6×7; Group BB: 9×5, 5×9; Group CC: 8×6, 6×8; Group DD: 7×7, 7×7; Group EE: 10×5, 5×10; Group FF: 9×6, 6×9; Group GG: 8×7, 7×8; Group HH: 10×6, 6×10; Group II: 9×7, 7×9; Group JJ: 8×8, 8×8; Group KK: 10×7, 7×10; Group LL: 9×8, 8×9; Group MM: 10×8, 8×10; Group NN: 9×9, 9×9; Group OO: 10×9, 9×10; and Group PP: 10×10, 10×10; and

[0028] N is at least 84. (Since A×B=B×A (where A is any number and B is any number), as used in the specification and claims, the multiplication operation “A×B” means A×B or its equivalent B×A. For example, the multiplication operation “7×6” means 7×6 or its equivalent 6×7.)

[0029] When the mathematical operation is a division operation, at least each of the following division operations is displayed on the playing faces of the playing cards:

[0030] Group A: 1÷1, 2÷2, 3÷3, 4÷4, 5÷5, 6÷6, 7÷7, 8÷8, 9÷9, 10÷10; Group B: 2÷1, 4÷2, 6÷3, 8÷4, 10÷5, 12÷6, 14÷7, 16÷8, 18÷9, 20÷10; Group C: 3÷1, 6÷2, 9÷3, 12÷4, 15÷5, 18÷6, 21÷7, 24÷8, 27÷9, 30÷10; Group D: 4÷1, 8÷2, 12÷3, 14÷4, 20÷5, 24÷6, 28÷7, 32÷8, 36÷9, 40÷10; Group E: 5÷1, 10÷2, 15÷3, 20÷4, 25÷5, 30÷6, 35÷7, 40÷8, 45÷9, 50÷10; Group F: 6÷1, 12÷2, 18÷3, 24÷4, 30÷5, 36÷6, 42÷7, 48÷8, 54÷9, 60÷10; Group G: 7÷1, 14÷2, 21÷3, 28÷4, 35÷5, 42÷6, 49÷7, 56÷8, 63÷9, 70÷10; Group H: 8÷1, 16÷2, 24÷3, 32÷4, 40÷5, 48÷6, 56÷7, 64÷8, 72÷9, 80÷10; Group I: 9÷1, 18÷2, 27÷3, 36÷4, 45÷5, 54÷6, 63÷7, 72÷8, 81÷9, 90÷10; and Group J: 10÷1, 20÷2, 30÷3, 40÷4, 50÷5, 60÷6, 70÷7, 80÷8, 90÷9, 100÷10: and N is at least 100.

[0031] In another embodiment of the invention, a deck of playing cards is provided for use in teaching young children to recognize the numerical value of (1) pictorial indicia (such as geometric shapes (e.g., circles, triangles, parallelograms, etc.) animal shapes, blank space, etc.) and (2) symbolic indicia (such as Arabic numerals, Roman numerals, Greek numerals, Chinese numerals, Korean numerals, Egyptian numerals, etc.). In this version of the invention, the deck comprises a first set of playing cards and a second set of playing cards, where (a) each playing card of each set comprises a playing face and a rear face, (b) the playing face of each playing card of the first set displays graphics comprising a pictorial indicia of numerical value, (c) the playing face of each playing card of the second set displays graphics comprising a symbolic indicia of numerical value, and (d) the pictorial indicia of numerical value displayed on any particular playing face of any particular playing card of the first set of playing cards has a corresponding symbolic indicia of the identical numerical value displayed on a playing face of one playing card of the second set of playing cards. Generally, the numerical value of the pictorial and symbolic indicia is within the range of at least whole numbers 1 through 10.

BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Exemplary playing cards of the present invention are shown in the drawings where the same number in the various figures represents the same element of the playing cards of the present invention and:

[0033]FIG. 1 depicts the playing faces (2 and 12) of an exemplary pair of addition playing cards (10A and 10B, respectively) where the playing faces (2 and 12) of the pair of playing cards (10A and 10B, respectively) display an addition operation (namely, 1, 1 a, and 1 b of addition playing card 10A and 11, 11 a, and 11 b of addition playing card 10B) having the same numerical value (which in the example shown is 5);

[0034]FIG. 2 depicts the playing faces (2 and 12) of an exemplary pair of subtraction playing cards (20A and 20B, respectively) where the playing faces (2 and 12) of the pair of playing cards (20A and 20B, respectively) display a subtraction operation (namely, 21, 21 a, and 21 b of subtraction playing card 20A and 22, 22 a, and 22 b of subtraction playing card 20B) having the same numerical value (which in the example shown is 5);

[0035]FIG. 3 depicts the playing faces (2 and 12) of an exemplary pair of multiplication playing cards (30A and 30B, respectively) where the playing faces (2 and 12) of the pair of playing cards (30A and 30B, respectively) display a multiplication operation (namely, 31, 31 a, and 31 b of multiplication playing card 30A and 32, 32 a, and 32 b of multiplication playing card 30B) having the same numerical value (which in the example shown is 40);

[0036]FIG. 4 depicts the playing faces (2 and 12) of an exemplary pair of division playing cards (40A and 40B, respectively) where the playing faces (2 and 12) of the pair of playing cards (40A and 40B, respectively) display a division operation (namely, 41, 41 a, and 41 b of division playing card 40A and 42, 42 a, and 42 b of division playing card 40B) having the same numerical value (which in the example shown is 10); and

[0037]FIG. 5 depicts the playing faces (2 and 12) of an exemplary pair of number recognition playing cards (playing card 50A being from a set of pictorial indicia playing cards and playing card 50B being from a set of symbolic indicia playing cards, respectively) where the numerical value of the pictorial indicia (51, 51 a, and 51 b) displayed on the playing face 2 of the pictorial indicia playing card 50A is numerically identical to the numerical value of the symbolic indicia (52, 52 a, and 52 b) displayed on the playing face 12 of the symbolic indicia playing card 50B (which in the example shown is 3).

DETAILED DESCRIPTION OF THE INVENTION

[0038] In a first embodiment of the present invention, a deck comprises N playing cards. With respect to FIG. 1, each playing card (such as addition playing cards 10A and 10B) comprises a playing face (such as playing faces 2 and 12, respectively) and a rear face (not shown). Each playing face (such as playing faces 2 and 12) displays graphics. The graphics displayed on any particular playing face (such as playing faces 2 and 12) of any particular playing card (such as addition playing cards 10A and 10B, respectively) comprise a representation of a mathematical operation (such as addition operation 1, 1 a, and 1 b of addition playing card 10A and addition operation 11, 11 a, and 11 b of addition playing card 10B) having a numerical value. An important feature of this embodiment of the present invention is that the mathematical operation (such as addition operation 1, 1 a, and 1 b) displayed on any particular playing face (such as playing face 2) of any particular playing card (such as addition playing card 10A) has a numerical value that is identical to the numerical value of a corresponding mathematical operation (such as addition operation 11, 11 a, and 11 b ) displayed on a playing face (such as playing face 12) of another playing card (such as addition playing card 10B).

[0039] Usually, the mathematical operation is selected from the group consisting of addition (such as shown in FIG. 1), subtraction (such as shown in FIG. 2), multiplication (such as shown in FIG. 3), and division (such as shown in FIG. 4). More specifically, the mathematical operation is selected from the group consisting of A+B (as illustrated in FIG. 1; and A+B=C), C−B (as illustrated in FIG. 2; and C−B=A), A×B (as illustrated in FIG. 3; and A×B=C), and C÷B (as illustrated in FIG. 4; and C÷B=A), where A is a number, B is a number, C is a number, and A and B are independent of one another.

[0040] An important feature of the present invention is that A, B, and C are selected from the group of numbers generally employed in teaching children basic addition, subtraction, multiplication, and division skills. For addition, subtraction, multiplication, and division playing cards, A and B are preferably independently selected from within the range of at least whole numbers 1 through 10, more preferably from within the range of at least whole numbers 0 to 10, and most preferably from within the range of 0 to 12. In addition, for division playing cards, C is a whole number determined by the equation C÷B=A.

[0041] Another important feature of the present invention is that the playing face of each playing card of the deck preferably displays a unique mathematical. (As used in the specification and claims, the terms “unique mathematical operation” means a mathematical operation (such as A+B, C−B, A×B, and C÷B) that is not identically duplicated on the playing face of any other playing card in the deck. For example, while 5+4 and 4+5 are equivalent addition operations, they are nevertheless unique mathematical operations with respect to one another because they are not identical.) However, in some circumstances it is not possible for the playing faces of the playing cards of a deck to display only unique mathematical operations and have the deck contain pairs of playing cards whose playing faces display corresponding mathematical operations having the identical numerical value. For example, since multiplication operation 1×1 cannot be duplicated by a unique mathematical operation, the multiplication deck must contain two playing cards whose playing faces display this multiplication operation.

[0042] The foregoing important features of the present invention are show below for addition, subtraction, multiplication, and division decks of playing cards.

[0043] For an addition deck of playing cards, at least each of the following addition operations is displayed on the playing faces of the playing cards of the deck: 1+1, A_(a)+B_(a); 2+1, A_(b)+B_(b); 1+3, 2+2; 1+4, 2+3; 1+5, 2+4, 3+3, A_(e)+B_(e); 1+6, 2+5, 3+4, A_(f)+B_(f); 1+7, 2+6, 4+4, 3+5; 1+8, 2+7, 3+6, 4+5; 1+9, 2+8, 3+7, 4+6, 5+5, A_(i)+B_(i); 1+10, 2+9, 3+8, 4+7, 5+6, A_(j)+B_(j); 2+10, 3+9, 4+8, 5+7, 6+6, A_(k)+B_(k); 3+10, 4+9, 5+8, 6+7; 4+10, 5+9, 6+8, 7+7; 5+10, 6+9, 7+8, A_(n)+B_(n); 6+10. 7+9, 8+8, A_(o)+B_(o); 7+10, 8+9; 8+10, 9+9; 9+10, A_(r)+B_(r); 10+10, and A_(s)+B_(s), where

[0044] A_(a)+B_(a) is selected from the group consisting of 1+1 and 2+0;

[0045] A_(b)+B_(b) is selected from the group consisting of 1+2 and 3+0;

[0046] A_(e)+B_(e) is selected from the group consisting of 5+1, 4+2, 6+0;

[0047] A_(f)+B_(f) is selected from the group consisting of 6+1, 5+2, 4+3, and 7+0;

[0048] A_(i)+B_(i) is selected from the group consisting of 9+1, 8+2, 7+3, 6+4, and 10+0;

[0049] A_(j)+B_(j) is selected from the group consisting of 10+1, 9+2, 8+3, 7+4, 6+5, and 11+0;

[0050] A_(k)+B_(k) is selected from the group consisting of 10+2, 9+3, 8+4, 7+5, and 12+0;

[0051] A_(n)+B_(n) is selected from the group consisting of 10+5, 9+6, 8+7, and 15+0;

[0052] A_(o)+B_(o) is selected from the group consisting of 10+6, 9+7, and 16+0;

[0053] A_(r)+B_(r) is selected from the group consisting of 10+9 and 19+0; and

[0054] A_(s)+B_(s) is selected from the group consisting of 10+10 and 20+0.

[0055] The above addition deck comprises at least 66 playing cards.

[0056] For a subtraction deck of playing cards, at least each of the following subtraction operations is displayed on the playing faces of the playing cards of the deck: 2−1, 3−2, 4−3, 5−4, 6−5, 7−6, 8−7, 9−10, 11−10; 3−1 4−2, 5−3, 6−4, 7−5, 8−6, 9−7, 10−8, 11−9, 12−10; 4−1, 5−2, 6−3, 7−4, 8−5, 9−6, 10−7, 11−8, 12−9; 13−10; 5−1, 6−2, 7−3, 8−4, 9−5, 10−6, 11−7, 12−8, 13−9; 14−10; 6−1, 7−2, 8−3, 9−4, 10−5, 11−6, 12−7, 13−8, 14−9; 15−10; 7−1, 8−2, 9−3, 10−4, 11−5, 12−6, 13−7, 14−8, 15−9; 16−10; 8−1, 9−2, 10−3, 11−4, 12−5, 13−6, 14−7, 15−8, 16−9; 17−10; 9−1, 10−2, 11−3, 12−4, 13−5, 14−6, 15−7, 16−8, 17−9; 18−10; 10−1, 11−2, 12−3, 13−4, 14−5, 15−6, 16−7, 17−8, 18−9; 19−10; 11−1, 12−2, 13−3, 14−4, 15−5, 16−6, 17−7, 18−8, 19−9, and 20−10. The above subtraction deck comprises at least 100 playing cards.

[0057] Preferably, the subtraction deck further comprises playing cards whose playing faces display the subtraction operations C₁−C₁ and C₂−C₂, where C₁ is any number, C₂ is any number, and the number of subtraction playing cards in the deck is at least 102. Alternatively, the subtraction deck preferably further comprises playing cards whose playing faces display the subtraction operations C₃−0 and C₃−0, where C₃ is any number and the number of subtraction playing cards in the deck is at least 102. Furthermore, the subtraction deck preferably further comprises playing cards whose playing faces display the subtraction operations C₁−C₁ and C₂−C₂ as well as C₃−0 and C₃−0, where C₁, C₂, and C₃ are as previously defined, and the number of subtraction playing cards in the deck is at least 104.

[0058] For a multiplication deck of playing cards, at least each of the following multiplication operations is displayed on the playing faces of the playing cards of the deck: 1×1, 1×1; 2×1, 1×2; 3×1, 1×3; 4×1, 2×2; 5×1, 1×5; 6×1 3×2; 7×1, 1×7; 8×1, 4×2; 9×1, 3×3; 10×1, 5×2; 6×2, 4×3; 7×2, 2×7; 5×3, 3×5; 8×2, 4×4; 9×2, 6×3; 10×2, 5×4; 7×3, 3×7; 8×3, 6×4; 5×5, 5×5; 9×3, 3×9; 7×4, 4×7; 10×3, 6×5; 8×4, 4×8; 7×5, 5×7; 9×4, 6×6; 10×4, 8×5; 7×6, 6×7; 9×5, 5×9; 8×6, 6×8; 7×7, 7×7; 10×5, 5×10; 9×6, 6×9; 8×7, 7×8; 10×6, 6×10; 9×7, 7×9; 8×8, 8×8; 10×7, 7×10; 9×8, 8×9; 10×8, 8×10; 9×9, 9×9; 10×9, 9×10; 10×10, and 10×10. The above multiplication deck comprises at least 84 playing cards.

[0059] Preferably, the multiplication deck further comprises playing cards whose playing faces display the multiplication operations C₁×0 and C₂×0, where C₁ and C₂ are as defined above and the number of multiplication playing cards in the deck is at least 86.

[0060] When the mathematical operation is a division operation, at least each of the following division operations is displayed on the playing faces of the playing cards: 1÷1, 2÷2, 3÷3, 4÷4, 5÷5, 6÷6, 7÷7, 8÷8, 9÷9, 10÷10; 2÷1, 4÷2, 6÷3, 8÷4, 10÷5, 12÷6, 14÷7, 16÷8, 18÷9, 20÷10; 3÷1, 6÷2, 9÷3, 12÷4, 15÷5, 18÷6, 21÷7, 24÷8, 27÷9, 30÷10; 4÷1, 8÷2, 12÷3, 14÷4, 20÷5, 24÷6, 28÷7, 32÷8, 36÷9, 40÷10; 5÷1, 10÷2, 15÷3, 20÷4, 25÷5, 30÷6, 35÷7, 40÷8, 45÷9, 50÷10; 6÷1, 12÷2, 18÷3, 24÷4, 30÷5, 36÷6, 42÷7, 48÷8, 54÷9, 60÷10; 7÷1, 14÷2, 21÷3, 28÷4, 35÷5, 42÷6, 49÷7, 56÷8, 63÷9, 70÷10; 8÷1, 16÷2, 24÷3, 32÷4, 40÷5, 48÷6, 56÷7, 64÷8, 72÷9, 80÷10; 9÷1, 18÷2, 27÷3, 36÷4, 45÷5, 54÷6, 63÷7, 72÷8, 81÷9, 90÷10; 10÷1, 20÷2, 30÷3, 40÷4, 50÷5, 60÷6, 70÷7, 80÷8, 90÷9, and 100÷10. The above division deck comprises at least 100 playing cards.

[0061] Preferably, the division deck further comprises playing cards whose playing faces display the division operations 0÷B₁ and 0÷B₂, where B₁ is any number, B₂ is any number, and the number of division playing cards in the deck is at least 102.

[0062] In another embodiment of the invention, a deck of playing cards is provided for use in teaching young children to recognize the numerical value of pictorial and symbolic indicia. As illustrated in FIG. 5, in this version of the invention, the deck comprises a first set of playing cards and a second set of playing cards. Each playing card of each set (such as playing card 50A of a first set and playing card 50B of a second set) comprises a playing face (such as playing face 2 of playing card 50A and playing face 12 of playing card 50B) and a rear face (not shown). The playing face of each playing card (such as playing face 2 of playing card 50A) of the first set displays graphics comprising a pictorial indicia of a numerical value (such as 51, 51 a, and 51 b). Similarly, the playing face of each playing card (such as playing face 12 of playing card 50B) of the second set displays graphics comprising a symbolic indicia of a numerical value (such as 52, 52 a, and 52 b). The pictorial indicia of numerical value (such as 51, 51 a, and 51 b) displayed on any particular playing face of any particular playing card (such as playing face 2 of playing card 50A) of the first set of playing cards has a corresponding symbolic indicia of the identical numerical value (such as 52, 52 a, and 52 b) displayed on a playing face of one playing card (such as playing face 12 of playing card 50B) of the second set of playing cards. This important element of the present invention is illustrated below in Table 1 for a deck of number recognition playing cards within the scope of the present invention.

[0063] The numerical value of the pictorial and symbolic indicia is selected from the group of numbers generally employed in teaching children to recognize the numerical value of pictorial and symbolic indicia. Accordingly, numerical value of the pictorial and symbolic indicia preferably cover all whole numbers with the range of 1 through 10, more preferably, all whole numbers within the range of 0 through 10, and, most preferably, all whole numbers within the range of 0 through 12.

[0064] Preferably, the playing face of each playing card of the first set (such as playing face 2 of indicia playing card 50A) displays a unique pictorial indicia of numerical value within the first set, and the playing face of each playing card of the second set (such as playing face 12 of symbolic playing card 50B) displays a unique symbolic indicia of numerical value within the second set. This preferred feature of the present invention is also shown in Table 1, infra, for a deck of number recognition playing cards within the scope of the present invention. TABLE 1 Corresponding Pairs of Unique Pictorial and Symbolic Indicia of Numerical Value Set Pictorial Symbolic Pictorial Symbolic Pictorial Symbolic 0 • 1 •• 2 ••• 3 •••• 4 ••••• 5 •••••• 6 ••••••• 7 •••••••• 8 ••••••••• 9 •••••••••• 10 ••••••••••• 11 •••••••••••• 12

[0065] The number recognition decks within the scope of the present invention generally comprises two, three, and typically no more than four sets of playing cards. When the number recognition deck comprises four sets of playing cards, preferably, the playing face of each playing card of the third set displays graphics comprising a pictorial indicia of a numerical value, the playing face of each playing card of the fourth set displays graphics comprising a symbolic indicia of a numerical value, and the pictorial indicia of numerical value displayed on any particular playing face of any particular playing card of the third set of playing cards has a corresponding symbolic indicia of identical numerical value displayed on a playing face of one playing card of the second and fourths set of playing cards.

[0066] In all embodiments of the present invention, the playing face of each playing card preferably has four corners and the graphics are displayed in the upright position on each playing card. More preferably, the graphics are displayed in the upright position in the upper left corner, the upper right corner, and in the body of the playing face of each playing card. For example, as shown in FIG. 1, the math operation (such as addition operation 1 of playing card 10A and addition operation 11 of playing card 10B) is displayed in the upright position in the body (such as bodies 8 and 18) of the playing face (such as playing faces 2 and 12, respectively) of the playing card (such as 10A and 10B, respectively). In addition, a smaller version of the math operation is also displayed in the upright position in the upper left hand corner (such as addition operation la displayed in upper left hand corner 3 and addition operation 11 a displayed in upper left hand corner 13) and in the upper right hand corner (such as addition operation 1 b displayed in upper right hand corner 4 and addition operation 11 b displayed in upper right hand corner 14) of each playing face of each playing card (such as playing faces 2 and 12 of playing cards 10A and 10B, respectively).

[0067] To help young children concentrate on the math operation shown on the playing faces (such 2 and 12) of the playing cards (such as 10A and 10B, respectively), the graphics on the playing faces (such as 2 and 12) preferably consist essentially of, and more preferably consist of, one or more depictions of the same math operation (such as math operation 1, 1 a, and 1 b on the playing face 2 of playing card 10A and math operation 11, 11 a, and 11 b on the playing face 12 of playing card 10B). In other words, the graphics displayed on the playing faces (such as 2 and 12) of the playing cards (such as 10A and 10B, respectively) are preferably substantially devoid, and more preferably totally devoid, of any other indicia other than the math operation (such as addition operations 1 and 11) shown in the body (such as 8 and 18, respectively), the same math operation (such as addition operations 1 a and 11 a) shown in the upper left hand corner (such as 3 and 13, respectively), and the same math operation (such as addition operations 1 b and 11 b) shown in the upper right hand corner (such as 4 and 14, respectively) of the playing face (such as 2 and 12, respectively) of the playing card (such as 10A and 10B, respectively).

[0068] To inform young children of the upright orientation of the playing faces (such as 2 and 12) of the playing cards (such as 10A and 10B, respectively) when the playing cards (such as 10A and 10B) are being dealt or taken playing face down from the deck, the rear faces (not shown) of the playing cards (such as 10A and 10B) preferably bear a design (not shown) that indicates the tops (such 5 and 15, respectively) of the playing cards (such a 10A and 10B). This preference enables young children to know which way the playing cards (such as 10A and 10B) should be placed in their hands to orient the playing faces (such as 2 and 12, respectively) of the playing cards (such as 10A and 10B) in the upright position prior to the children seeing the playing faces (such as 2 and 12) of the playing cards (such as 10A and 10B).

[0069] The playing cards (such as 10A and 10B) are preferably the size of standard poker cards (i.e., about 3.5 inches (8.89 cm) high by about 2.5 inches (6.95 cm) wide), but playing cards varying by about ±1 inch (2.54 cm) in height and about ±0.5 inch (1.27 cm) in width, and generally by not more than about ±0.5 inch (1.27 cm) in height and not more than about ±0.25 inch (0.635 cm) in width, can also be used.

[0070] Optionally, the decks of the present invention can also comprise one, two, or more (i) Joker cards and/or (ii) instructional cards (e.g., cards that contain rules for playing card games) and/or (iii) informational cards (e.g., cards containing miscellaneous information) and/or reference cards (e.g., cards containing answers to mathematical operations or showing the correlation between pictorial and symbolic indicia of numerical values). (The Joker, instructional, informational, and references cards are not “playing cards” as that term is defined above and used in the specification and claims.)

[0071] The decks of the present invention can be manufactured by techniques well know to those skilled in the art.

[0072] A game preferably consists essentially of, and more preferably consists of, a deck comprising the playing cards. In other words, other than the playing cards, the Joker card(s), the instructional card(s), the informational card(s), the reference card(s) and the box(es) or other means used to house or hold the deck of playing cards, the game of the present invention is preferably substantially devoid, and more preferably totally devoid, of any other items (such as playing boards, etc.).

[0073] The decks of playing cards of the present invention can be used by themselves to play numerous well know card games. When a deck consists of only two sets (or only pairs) of matching playing cards, some of the well known matching card games can be played as described below.

Concentration (a.k.a. Memory)

[0074] Pairs of playing cards are shuffled and placed face down in a grid. Two or more pairs of cards can be used to form the grid. The larger the grid, the more challenging the game. It is recommended that when playing Concentration for the first time with a player, start the grid relatively small and increase the grid with each subsequent round until a grid size that is challenging, but not overwhelming, is found.

[0075] Players take turns turning over two cards. The cards are turned over in their places and the faces of the turned over cards should be visible to all the players. If the numerical value of the turned over cards match, the player removes the matching cards from the grid and goes again. If the turned over cards do not match, the player returns the played cards to their face down position and play advances to the next player.

[0076] When all the cards in the grid have been matched, the player with the most pairs of cards wins that round of Concentration. Concentration continues until one of the following endpoints:

[0077] i. Entire Deck Played Once: Once the entire deck has been played once, the winner is the player who won the most rounds.

[0078] ii. Predetermined Number of Rounds: The first player to win a predetermined number of rounds wins.

Go Fish

[0079] Each player is dealt 7 cards face down. The undealt cards are placed in a pile face down, preferably within reach of all the players.

[0080] Each player picks up the cards dealt to him or her and organizes them in his or her hand. If any player finds one or more pairs of cards in his or her hand having the same numerical value, the player shows the pair to the other players, says the numerical value of the pair of cards, and places the pair face up or face down in front of him or her.

[0081] Play proceeds in the clockwise or counterclockwise direction beginning with the player to one side of the dealer. The player whose turn it is asks the other players if they have a card that matches a card in that player's hand. (For example, the player may ask, “Does anyone have a 5?”) If one of the other players has that card in his or her hand, the card is handed over the player who asked for it, that player removes the matching card from his or her hand to form a pair, and again asks for another card that matches a card in the player's hand. However, when the player asks for a card and no other player has that card, the other players say “go fish,” the player whose turn it is takes the top card from the pile of undealt cards, and play advances to the next player. (If the card taken from the pile matches any card in the player's hand, the player shows the pair to the other players, says the numerical value of the pair of cards, and places them face up or face down in front of him or her, but play still advances to the next player.)

[0082] Go Fish ends when either of the following occurs first:

[0083] i. One player no longer has any cards in his or her hand: When a player no longer has any cards in his or her hand, the other players subtract the number of cards remaining in their hands from the number of cards in their group of matched pairs, and the player with the most cards in his or her remaining group of matched pairs wins the game. ii. Pile of undealt cards exhausted: When the pile undealt cards is exhausted, all the players subtract the number of cards remaining in their hands from the number of cards in their group of matched pairs, and the player with the most cards in his or her remaining group of matched pairs wins the game.

Old Maid

[0084] The entire deck consisting of all the math cards plus one Joker is dealt face down between all the players.

[0085] Each player picks up the cards dealt to him or her and organizes them in his or her hand so that each player can quickly determine (a) whether he or she already holds any matched pairs of cards and (b) whether he or she acquires a card during the game that matches (i.e., has the same numerical value as) a card already in his or her hand. If any player finds one or more matching pairs of cards in his or her hand, that player shows the pair to the other players, says the numerical value of the pair of cards, and places them face up or face down in front of him or her.

[0086] Play proceeds in the clockwise or counterclockwise direction beginning with the player to one side of the dealer. The player whose turn it is takes one card from the play next to him or her in the direction that play is advancing. If the player picks a card that matches a card in his or her hand, that player removes the matching card from his or her hand to form a pair, shows the pair to the other players, states the numerical value on the face of the pair of cards, and puts the matched pair of cards down. Whether or not the player was able to make a match, play advances to the next player.

[0087] Old Maid ends when all the players, except the player holding the Joker (i.e., the Old Maid), no longer have any cards in their hands.

Rummy

[0088] Play begins with one well-shuffled deck that includes the 2 Jokers (the Jokers are wild, i.e., they can represent any number). Each player is dealt 10 cards. The remaining cards are placed face down in a pile on a table to form the stock.

[0089] A player can do one or more of the following during his or her turn:

[0090] 1. Use two or more cards from his or her hand to form one or more:

[0091] a. Pairs (such as “1, 1” and “5, 5”);

[0092] b. Sequences of at least 3 members (such as straight sequence 1, 2, 3 and wrap around sequence 11, 12, 1); and/or

[0093] c. Progressions of at least 3 members (e.g., linear progressions such as 2, 4, 6 (i.e., 2N), exponential progressions such as 1, 4, 9 (i.e., N²), and primary number progressions such as 1, 3, 5, 7); and/or

[0094] 2. Add a card from his or her hand to a sequence or progression on the table; and/or

[0095] 3. Use one or more of his or her cards in conjunction with one or more cards already on the table to form one or more new pairs, sequences, and/or progressions, provided that the card(s) from the player's hand and all the cards that were on the table at the beginning of that players turn form either pairs, sequences, and/or progressions at the end of that players turn.

[0096] When a player can do none of the above, the player must take the top card from the stock.

[0097] The first player to dispose of all of his or her cards wins. If none of the players has disposed of all his or her cards by the time the stock is depleted, the game ends in a draw.

Gin Rummy

[0098] Play begins with one well-shuffled deck minus the Jokers. Each player is dealt 7 cards. The remaining cards are placed face down in a pile on a table to form the stock. The top card of the stock is placed on the surface face up and becomes the first card of the discard pile.

[0099] A player must take either the top card of the stock or the top face up card of the discard pile. Play then advances to the next player.

[0100] The cards are held in each player's hand until the winning player is able to employ all 7 cards in his or her hand in either one or more:

[0101] 1. Pairs (“1, 1” and “5, 5”);

[0102] 2. Sequences of at least 3 members (such as straight sequence 1, 2, 3 and wrap around sequence 11, 12, 1); and/or

[0103] 3. Progressions of at least 3 members (e.g., linear progressions such as 2, 4, 6 (i.e., 2N), exponential progressions such as 1, 4, 9 (i.e., N²), and primary number progressions such as 1, 3, 5, 7).

[0104] The winning player discards 1 card from his or her hand, says Rummy, places the 7 remaining cards face up on the table, and identifies the pairs, sequences, and/or progressions.

[0105] If none of the players is able to declare Rummy before the stock is depleted, the game ends in a draw.

[0106] While the preferred embodiments of the invention have been set forth above in detail, some modifications can be made to the preferred versions without departing from the spirit of the present invention. For example, the graphics of the mathematical operation and/or pictorial or symbolic indicia of numerical value can be displayed (1) in the inverted and upright positions on the playing face of the playing cards, (2) in one, two, three, or all four corners on the playing faces of four-cornered playing cards (whether or not the graphics are also displayed in the body of the playing faces of the playing cards), and (3) on the playing faces of 3-, 5-, 6- or more cornered playing cards. Also, mathematical operations can be represented by means other than those shown in FIGS. 1 through 4 and in the specification, supra. For example, a multiplication operation can also be represented by A·B and by (A)(B) and a division operation can be represented by A/B. Furthermore, combinations of A and B not shown above can also be employed on addition, subtraction, and multiplication playing cards within the scope of the present invention and combinations of C and B not shown in above can also be employed on division playing cards within the scope of the present invention. Likewise, pictorial and symbolic indicia not shown above can also be employed on the pictorial and symbolic indicia playing cards, respectively, of the present invention. Accordingly, the foregoing alternative embodiments are included within the scope of the present invention. 

What is claimed is:
 1. A deck comprising N playing cards, where: a. each playing card comprises a playing face and a rear face; b. each playing face displays graphics; c. the graphics displayed on any particular playing face of any particular playing card comprises a representation of a single mathematical operation having a numerical value; and d. the mathematical operation is selected from the group consisting of addition, subtraction, multiplication, and division, where: i. when the mathematical operation is an addition operation, at least each of the following addition operations is displayed on the playing faces of the playing cards:: 1+1, A_(a)+B_(a); 2+1, A_(b)+B_(b); 1+3, 2+2; 1+4, 2+3; 1+5, 2+4, 3+3, A_(e)+B_(e); 1+6, 2+5, 3+4, A_(f)+B_(f); 1+7, 2+6, 4+4, 3+5; 1+8, 2+7, 3+6, 4+5; 1+9, 2+8, 3+7, 4+6, 5+5, A_(i)+B_(i); 1+10, 2+9, 3+8, 4+7, 5+6, A_(j)+B_(j); 2+10, 3+9, 4+8, 5+7, 6+6, A_(k)+B_(k); 3+10, 4+9, 5+8, 6+7; 4+10, 5+9, 6+8, 7+7; 5+10, 6+9, 7+8, A_(n)+B_(n); 6+10. 7+9, 8+8, A_(o)+B_(o); 7+10, 8+9; 8+10, 9+9; 9+10, A_(r)+B_(r); 10+10, and A_(s)+B_(s); A_(a)+B_(a) is selected from the group consisting of 1+1 and 2+0; A_(b)+B_(b) is selected from the group consisting of 1+2 and 3+0; A_(e)+B_(e) is selected from the group consisting of 5+1, 4+2, 6+0; A_(f)+B_(f) is selected from the group consisting of 6+1, 5+2, 4+3, and 7+0; A_(i)+B_(i) is selected from the group consisting of 9+1, 8+2, 7+3, 6+4, and 10+0; A_(j)+B_(j) is selected from the group consisting of 10+1, 9+2, 8+3, 7+4, 6+5, and 11+0; A_(k)+B_(k) is selected from the group consisting of 10+2, 9+3, 8+4, 7+5, and 12+0; A_(n)+B_(n) is selected from the group consisting of 10+5, 9+6, 8+7, and 15+0; A_(o)+B_(o) is selected from the group consisting of 10+6, 9+7, and 16+0; A_(r)+B_(r) is selected from the group consisting of 10+9 and 19+0; and A_(s)+B_(s) is selected from the group consisting of 10+10 and 20+0; and N is at least 66; ii. when the mathematical operation is a subtraction operation, at least each of the following subtraction operations is displayed on the playing faces of the playing cards:2−1, 3−2, 4−3, 5−4, 6−5, 7−6, 8−7, 9−10, 11−10; 3−1, 4−2, 5−3, 6−4, 7−5, 8−6, 9−7, 10−8, 11−9, 12−10; 4−1, 5−2, 6−3, 7−4, 8−5, 9−6, 10−7, 11−8, 12−9; 13−10; 5−1, 6−2, 7−3, 8−4, 9−5, 10−6, 11−7, 12−8, 13−9; 14−10; 6−1, 7−2, 8−3, 9−4, 10−5, 11−6, 12−7, 13−8, 14−9; 15−10; 7−1, 8−2, 9−3, 10−4, 11−5, 12−6, 13−7, 14−8, 15−9; 16−10; 8−1, 9−2, 10−3, 11−4, 12−5, 13−6, 14−7, 15−8, 16−9; 17−10; 9−1, 10−2, 11−3, 12−4, 13−5, 14−6, 15−7, 16−8, 17−9; 18−10; 10−1, 11−2, 12−3, 13−4, 14−5, 15−6, 16−7, 17−8, 18−9; 19−10; 11−1, 12−2, 13−3, 14−4, 15−5, 16−6, 17−7, 18−8, 19−9, and 20−10; and N is at least 100; iii. when the mathematical operation is a multiplication operation, at least each of the following multiplication operations is displayed on the playing faces of the playing cards: 1×1, 1×1; 2×1, 1×2; 3×1, 1×3; 4×1, 2×2; 5×1, 1×5; 6×1, 3×2; 7×1, 1×7; 8×1, 4×2; 9×1, 3×3; 10×1, 5×2; 6×2, 4×3; 7×2, 2×7; 5×3, 3×5; 8×2, 4×4; 9×2, 6×3; 10×2, 5×4; 7×3, 3×7; 8×3, 6×4; 5×5, 5×5; 9×3, 3×9; 7×4, 4×7; 10×3, 6×5; 8×4, 4×8; 7×5, 5×7; 9×4, 6×6; 10×4, 8×5; 7×6, 6×7; 9×5, 5×9; 8×6, 6×8; 7×7, 7×7; 10×5, 5×10; 9×6, 6×9; 8×7, 7×8; 10×6, 6×10; 9×7, 7×9; 8×8, 8×8; 10×7, 7×10; 9×8, 8×9; 10×8, 8×10; 9×9, 9×9; 10×9, 9×10; and 10×10, and 10×10; and N is at least 84; and iv. when the mathematical operation is a division operation, at least each of the following division operations is displayed on the playing faces of the playing cards: 1÷1, 2÷2, 3÷3, 4÷4, 5÷5, 6÷6, 7÷7, 8÷8, 9÷9, 10÷10; 2÷1, 4÷2, 6÷3, 8÷4, 10÷5, 12÷6, 14÷7, 16÷8, 18÷9, 20÷10; 3÷1, 6÷2, 9÷3, 12÷4, 15÷5, 18÷6, 21÷7, 24÷8, 27÷9, 30÷10; 4÷1, 8÷2, 12÷3, 14÷4, 20÷5, 24÷6, 28÷7, 32÷8, 36÷9, 40÷10; 5÷1, 10÷2, 15÷3, 20÷4, 25÷5, 30÷6, 35÷7, 40÷8, 45÷9, 50÷10; 6÷1, 12÷2, 18÷3, 24÷4, 30÷5, 36÷6, 42÷7, 48÷8, 54÷9, 60÷10; 7÷1, 14÷2, 21÷3, 28÷4, 35÷5, 42÷6, 49÷7, 56÷8, 63÷9, 70÷10; 8÷1, 16÷2, 24÷3, 32÷4, 40÷5, 48÷6, 56÷7, 64÷8, 72÷9, 80÷10; 9÷1, 18÷2, 27÷3, 36÷4, 45÷5, 54÷6, 63÷7, 72÷8, 81÷9, 90÷10; 10÷1, 20÷2, 30÷3, 40÷4, 50÷5, 60÷6, 70÷7, 80÷8, 90÷9, and 100÷10; and N is at least
 100. 2. The deck of claim 1 where: the mathematical operation is an addition operation; at least each of the following addition operations is displayed on the playing faces of the playing cards: 1+1, A_(a)+B_(a); 2+1, A_(b)+B_(b); 1+3, 2+2; 1+4, 2+3; 1+5, 2+4, 3+3, A_(e)+B_(e); 1+6, 2+5, 3+4, A_(f)+B_(f); 1+7, 2+6, 4+4, 3+5; 1+8, 2+7, 3+6, 4+5; 1+9, 2+8, 3+7, 4+6, 5+5, A_(i)+B_(i); 1+10, 2+9, 3+8, 4+7, 5+6, A_(j)+B_(j); 2+10, 3+9, 4+8, 5+7, 6+6, A_(k)+B_(k); 3+10, 4+9, 5+8, 6+7; 4+10, 5+9, 6+8, 7+7; 5+10, 6+9, 7+8, A_(n)+B_(n); 6+10. 7+9, 8+8, A_(o)+B_(o); 7+10, 8+9; 8+10, 9+9; 9+10, A_(r)+B_(r); 10+10, and A_(s)+B_(s); A_(a)+B_(a) is selected from the group consisting of 1+1 and 2+0; A_(b)+B_(b) is selected from the group consisting of 1+2 and 3+0; A_(e)+B_(e) is selected from the group consisting of 5+1, 4+2, 6+0; A_(f)+B_(f) is selected from the group consisting of 6+1, 5+2, 4+3, and 7+0; A_(i)+B_(i) is selected from the group consisting of 9+1, 8+2, 7+3, 6+4, and 10+0; A_(j)+B_(j) is selected from the group consisting of 10+1, 9+2, 8+3, 7+4, 6+5, and 11+0; A_(k)+B_(k) is selected from the group consisting of 10+2, 9+3, 8+4, 7+5, and 12+0; A_(n)+B_(n) is selected from the group consisting of 10+5, 9+6, 8+7, and 15+0; A_(o)+B_(o) is selected from the group consisting of 10+6, 9+7, and 16+0; A_(r)+B_(r) is selected from the group consisting of 10+9 and 19+0; A_(s)+B_(s) is selected from the group consisting of 10+10 and 20+0; and N is at least
 66. 3. The deck of claim 1 where: the mathematical operation is a subtraction operation; at least each of the following subtraction operations is displayed on the playing faces of the playing cards: 2−1, 3−2, 4−3, 5−4, 6−5, 7−6, 8−7, 9−10, 11−10; 3−1, 4−2, 5−3, 6−4, 7−5, 8−6, 9−7, 10−8, 11−9, 12−10; 4−1, 5−2, 6−3, 7−4, 8−5, 9−6, 10−7, 11−8, 12−9; 13−10; 5−1, 6−2, 7−3, 8−4, 9−5, 10−6, 11−7, 12−8, 13−9; 14−10; 6−1, 7−2, 8−3, 9−4, 10−5, 11−6, 12−7, 13−8, 14−9; 15−10; 7−1, 8−2, 9−3, 10−4, 11−5, 12−6, 13−7, 14−8, 15−9; 16−10; 8−1, 9−2, 10−3, 11−4, 12−5, 13−6, 14−7, 15−8, 16−9; 17−10; 9−1, 10−2, 11−3, 12−4, 13−5, 14−6, 15−7, 16−8, 17−9; 18−10; 10−1, 11−2, 12−3, 13−4, 14−5, 15−6, 16−7, 17−8, 18−9; 19−10; 11−1, 12−2, 13−3, 14−4, 15−5, 16−6, 17−7, 18−8, 19−9, and 20−10; and N is at least
 100. 4. The deck of claim 1 where: the mathematical operation is a subtraction operation; at least each of the following subtraction operations is displayed on the playing faces of the playing cards: 2−1, 3−2, 4−3, 5−4, 6−5, 7−6, 8−7, 9−10, 11−10; 3−1, 4−2, 5−3, 6−4, 7−5, 8−6, 9−7, 10−8, 11−9, 12−10; 4−1, 5−2, 6−3, 7−4, 8−5, 9−6, 10−7, 11−8, 12−9; 13−10; 5−1, 6−2, 7−3, 8−4, 9−5, 10−6, 11−7, 12−8, 13−9; 14−10; 6−1, 7−2, 8−3, 9−4, 10−5, 11−6, 12−7, 13−8, 14−9; 15−10; 7−1, 8−2, 9−3, 10−4, 11−5, 12−6, 13−7, 14−8, 15−9; 16−10; 8−1, 9−2, 10−3, 11−4, 12−5, 13−6, 14−7, 15−8, 16−9; 17−10; 9−1, 10−2, 11−3, 12−4, 13−5, 14−6, 15−7, 16−8, 17−9; 18−10; 10−1, 11−2, 12−3, 13−4, 14−5, 15−6, 16−7, 17−8, 18−9; 19−10; 11−1, 12−2, 13−3, 14−4, 15−5, 16−6, 17−7, 18−8, 19−9, and 20−10; and the deck further comprises playing cards whose playing faces display the subtraction operations C₁−C₁ and C₂−C₂; C₁ is any number; C₂ is any number; and N is at least
 102. 5. The deck of claim 1 where: the mathematical operation is a subtraction operation; at least each of the following subtraction operations is displayed on the playing faces of the playing cards: 2−1, 3−2, 4−3, 5−4, 6−5, 7−6, 8−7, 9−10, 11−10; 3−1, 4−2, 5−3, 6−4, 7−5, 8−6, 9−7, 10−8, 11−9, 12−10; 4−1, 5−2, 6−3, 7−4, 8−5, 9−6, 10−7, 11−8, 12−9; 13−10; 5−1, 6−2, 7−3, 8−4, 9−5, 10−6, 11−7, 12−8, 13−9; 14−10; 6−1, 7−2, 8−3, 9−4, 10−5, 11−6, 12−7, 13−8, 14−9; 15−10; 7−1, 8−2, 9−3, 10−4, 11−5, 12−6, 13−7, 14−8, 15−9; 16−10; 8−1, 9−2, 10−3, 11−4, 12−5, 13−6, 14−7, 15−8, 16−9; 17−10; 9−1, 10−2, 11−3, 12−4, 13−5, 14−6, 15−7, 16−8, 17−9; 18−10; 10−1, 11−2, 12−3, 13−4, 14−5, 15−6, 16−7, 17−8, 18−9; 19−10; 11−1, 12−2, 13−3, 14−4, 15−5, 16−6, 17−7, 18−8, 19−9, and 20−10; and the deck further comprises playing cards whose playing faces display the subtraction operations C₁−0 and C₁−0; C₁ is any number; and N is at least
 102. 6. The deck of claim 1 where: the mathematical operation is a multiplication operation; at least each of the following multiplication operations is displayed on the playing faces of the playing cards: 1×1, 1×1; 2×1, 1×2; 3×1, 1×3; 4×1, 2×2; 5×1, 1×5; 6×1, 3×2; 7×1, 1×7; 8×1, 4×2; 9×1, 3×3; 10×1, 5×2; 6×2, 4×3; 7×2, 2×7; 5×3, 3×5; 8×2, 4×4; 9×2, 6×3; 10×2, 5×4; 7×3, 3×7; 8×3, 6×4; 5×5, 5×5; 9×3, 3×9; 7×4, 4×7; 10×3, 6×5; 8×4, 4×8; 7×5, 5×7; 9×4, 6×6; 10×4, 8×5; 7×6, 6×7; 9×5, 5×9; 8×6, 6×8; 7×7, 7×7; 10×5, 5×10; 9×6, 6×9; 8×7, 7×8; 10×6, 6×10; 9×7, 7×9; 8×8, 8×8; 10×7, 7×10; 9×8, 8×9; 10×8, 8×10; 9×9, 9×9; 10×9, 9×10; and 10×10, and 10×10; and N is at least
 84. 7. The deck of claim 1 where: the mathematical operation is a multiplication operation; at least each of the following multiplication operations is displayed on the playing faces of the playing cards: 1×1, 1×1; 2×1, 1×2; 3×1, 1×3; 4×1, 2×2; 5×1, 1×5; 6×1, 3×2; 7×1, 1×7; 8×1, 4×2; 9×1, 3×3; 10×1, 5×2; 6×2, 4×3; 7×2, 2×7; 5×3, 3×5; 8×2, 4×4; 9×2, 6×3; 10×2, 5×4; 7×3, 3×7; 8×3, 6×4; 5×5, 5×5; 9×3, 3×9; 7×4, 4×7; 10×3, 6×5; 8×4, 4×8; 7×5, 5×7; 9×4, 6×6; 10×4, 8×5; 7×6, 6×7; 9×5, 5×9; 8×6, 6×8; 7×7, 7×7; 10×5, 5×10; 9×6, 6×9; 8×7, 7×8; 10×6, 6×10; 9×7, 7×9; 8×8, 8×8; 10×7, 7×10; 9×8, 8×9; 10×8, 8×10; 9×9, 9×9; 10×9, 9×10; and 10×10, and 10×10; and the deck further comprises playing cards whose playing faces display the multiplication operations C₁×0 and C₂×0; C₁ is any number; C₂ is any number; and N is at least
 86. 8. The deck of claim 1 where: the mathematical operation is a division operation; at least each of the following division operations is displayed on the playing faces of the playing cards: 1÷1, 2÷2, 3÷3, 4÷4, 5÷5, 6÷6, 7÷7, 8÷8, 9÷9, 10÷10; 2÷1, 4÷2, 6÷3, 8÷4, 10÷5, 12÷6, 14÷7, 16÷8, 18÷9, 20÷10; 3÷1, 6÷2, 9÷3, 12÷4, 15÷5, 18÷6, 21÷7, 24÷8, 27÷9, 30÷10; 4÷1, 8÷2, 12÷3, 14÷4, 20÷5, 24÷6, 28÷7, 32÷8, 36÷9, 40÷10; 5÷1, 10÷2, 15÷3, 20÷4, 25÷5, 30÷6, 35÷7, 40÷8, 45÷9, 50÷10; 6÷1, 12÷2, 18÷3, 24÷4, 30÷5, 36÷6, 42÷7, 48÷8, 54÷9, 60÷10; 7÷1, 14÷2, 21÷3, 28÷4, 35÷5, 42÷6, 49÷7, 56÷8, 63÷9, 70÷10; 8÷1, 16÷2, 24÷3, 32÷4, 40÷5, 48÷6, 56÷7, 64÷8, 72÷9, 80÷10; 9÷1, 18÷2, 27÷3, 36÷4, 45÷5, 54÷6, 63÷7, 72÷8, 81÷9, 90÷10; 10÷1, 20÷2, 30÷3, 40÷4, 50÷5, 60÷6, 70÷7, 80÷8, 90÷9, and 100÷10; and N is at least
 100. 9. The deck of claim 1 where: the mathematical operation is a division operation; at least each of the following division operations is displayed on the playing faces of the playing cards: 1÷1, 2÷2, 3÷3, 4÷4, 5÷5, 6÷6, 7÷7, 8÷8, 9÷9, 10÷10; 2÷1, 4÷2, 6÷3, 8÷4, 10÷5, 12÷6, 14÷7, 16÷8, 18÷9, 20÷10; 3÷1, 6÷2, 9÷3, 12÷4, 15÷5, 18÷6, 21÷7, 24÷8, 27÷9, 30÷10; 4÷1, 8÷2, 12÷3, 14÷4, 20÷5, 24÷6, 28÷7, 32÷8, 36÷9, 40÷10; 5÷1, 10÷2, 15÷3, 20÷4, 25÷5, 30÷6, 35÷7, 40÷8, 45÷9, 50÷10; 6÷1, 12÷2, 18÷3, 24÷4, 30÷5, 36÷6, 42÷7, 48÷8, 54÷9, 60÷10; 7÷1, 14÷2, 21÷3, 28÷4, 35÷5, 42÷6, 49÷7, 56÷8, 63÷9, 70÷10; 8÷1, 16÷2, 24÷3, 32÷4, 40÷5, 48÷6, 56÷7, 64÷8, 72÷9, 80÷10; 9÷1, 18÷2, 27÷3, 36÷4, 45÷5, 54÷6, 63÷7, 72÷8, 81÷9, 90÷10; 10÷1, 20÷2, 30÷3, 40÷4, 50÷5, 60÷6, 70÷7, 80÷8, 90÷9, and 100÷10; and the deck further comprises playing cards whose playing faces display the division operations 0÷B₁ and 0÷B₂; B₁ is any number; B₂ is any number; and N is at least
 102. 10. The deck of claim 1 further comprising at least one card selected from the group consisting of joker, instructional, reference, any other non-playing card, and combinations thereof.
 11. The deck of claim 1 where: each playing card has four corners and the graphics are displayed in the upright position on the playing face of each playing card.
 12. The deck of claim 1 where: each playing card has four corners; the graphics are displayed in the upright position in the upper left hand corner, the upper right hand corner, and the body of the playing face of each playing card.
 13. A deck of playing cards comprising a first set of playing cards and a second set of playing cards, where: a. each playing card of each set comprises a playing face and a rear face; b. the playing face of each playing card of the first set displays graphics comprising a pictorial indicia of a numerical value; c. the playing face of each playing card of the second set displays graphics comprising a symbolic indicia of a numerical value; and d. the pictorial indicia of numerical value displayed on any particular playing face of any particular playing card of the first set of playing cards has a corresponding symbolic indicia of identical numerical value displayed on a playing face of one playing card of the second set of playing cards.
 14. The deck of claim 13 where: the playing face of each playing card of the first set displays a pictorial indicia of unique numerical value within the first set of playing cards and the playing face of each playing card of the second set displays a symbolic indicia of unique numerical value within the second set of playing cards.
 15. The deck of claim 13 where: the first set of playing cards comprises at least 10 playing cards and the unique numerical value of the pictorial indicia displayed on any particular playing face of any particular playing card of the first set of playing cards is within the range of at least whole numbers 1 through 10; and the second set of playing cards comprises at least 10 playing cards and the unique numerical value of the symbolic indicia displayed on any particular playing face of any particular playing card of the first set of playing cards is within the range of at least whole numbers 1 through
 10. 16. The deck of claim 13 where: the first set of playing cards comprises at least 11 playing cards and the unique numerical value of the pictorial indicia displayed on any particular playing face of any particular playing card of the first set of playing cards is within the range of at least whole numbers 0 through 10; and the second set of playing cards comprises at least 11 playing cards and the unique numerical value of the symbolic indicia displayed on any particular playing face of any particular playing card of the first set of playing cards is within the range of at least whole numbers 0 through
 10. 17. The deck of claim 13 where: the first set of playing cards comprises at least 13 playing cards and the unique numerical value of the pictorial indicia displayed on any particular playing face of any particular playing card of the first set of playing cards is within the range of at least whole numbers 0 through 12; and the second set of playing cards comprises at least 13 playing cards and the unique numerical value of the symbolic indicia displayed on any particular playing face of any particular playing card of the first set of playing cards is within the range of at least whole numbers 0 through
 12. 18. The deck of claim 13 further comprising a third set of playing cards and a fourth set of playing cards, where: e. the playing face of each playing card of the third set displays graphics comprising a pictorial indicia of a numerical value; f. the playing face of each playing card of the fourth set displays graphics comprising a symbolic indicia of a numerical value; and g. the pictorial indicia of numerical value displayed on any particular playing face of any particular playing card of the third set of playing cards has a corresponding symbolic indicia of the identical numerical value displayed on a playing face of one playing card of the second and fourth sets of playing cards.
 19. The deck of claim 13 where: each playing card has four corners and the graphics are displayed in the upright position on the playing face of each playing card.
 20. The deck of claim 13 further comprising at least one card selected from the group consisting of joker, instructional, reference, any other non-playing card, and combinations thereof. 